Labour leadership frontrunner Jeremy Corbyn has unveiled plans to give grants to working-class party members to help them become MPs to stop it being dominated by people from affluent backgrounds.

Data from his campaign team claims Labour now has more MPs who went to private school – around 12% – than those from manual working backgrounds.

Corbyn would set up a diversity fund to help party members who are shortlisted in one of the top 100 target seats at the next election while they are trying to win selection. Campaign costs can amount to £4,500, his team claims.

Corbyn said: “If the party is to win back the 5 million predominantly working-class voters lost since 1997, then we must reflect those we seek to represent. It is not enough to be for working people – we have to be of working people as well.

“Because if at the next election we as a party have hardly any candidates from the frontline of Tory cuts then it will be very hard to be heard by voters we need to win back.

“It is therefore only right that the party helps collectively to shoulder some of the financial burden of members on more modest incomes during the candidate selection process so that we remain the people’s party.”

Meanwhile, leadership rival Yvette Cooper will set out her plans to tackle climate change, warning it is the “biggest existential challenge threat to mankind”. She will outline an environmental blueprint that includes plans to ensure every new home is a zero-carbon building.

At an event in Leicester, Cooper will say: “Climate change is the biggest existential challenge threat to mankind. There are some who believe that the impact of climate change will be felt far off in the distant future, if at all, and as a result we can defer acting to stop it now. They’re wrong. The consequences of the government’s inaction are being felt here and now. They are a betrayal of future generations.”

She will add: “David Cameron’s hug-a-husky but scrap-a-windfarm hypocrisy has set us back years and puts us in danger. The government is failing to show the leadership required and seems set on undermining the green economy.”